Are there residency requirments to obtain a divorce in the State of Michigan?

Yes.  You must meet the residency requirements before you may be granted a divorce in the State of Michigan.

The relevant statute, MCL 552.9 provides as follows:
(1) A judgment of divorce shall not be granted by a court in this state in an action for divorce unless the complainant or defendant has resided in this state for 180 days immediately preceding the filing of the complaint and, except as otherwise provided in subsection (2), the complainant or defendant has resided in the county in which the complaint is filed for 10 days immediately preceding the filing of the complaint.